Algorithms for least‐squares linear prediction and maximum entropy spectral analysis—Part II: Fortran program

Abstract

We present a set of Fortran subroutines which implement the least‐squares algorithm described in Part I (Barrodale and Erickson, 1980, this issue) for solving three variants of the linear prediction problem. When combined with a suitable driver program, these subroutines can be used to calculate maximum entropy spectra without imposing a Toeplitz structure on the model.

The quasi-periodic fluctuations in the drought indices over the North American Great Plains

“…The coefficients of the filter are then applied to the timeseries as the weightings in a running mean, and this ideally removes all the predictable portions of the signal, thus leaving only the noise. We used the optimal least squares algorithm of Barrodale and Erickson (1980) to obtain the filter coefficients and the output of Equation (4). The algorithm minimizes the sum of squares of the forward and backward one-step prediction errors.…”

Geodynamic Research at the Department of Planetary Geodesy, SRC PAS

“…Moreover, the autoregressive model in the LS+AR combination is more tuned to higher frequency variations than to frequency variations corresponding to the annual and Chandler frequency band. The autoregressive coefficients in the autoregressive model were estimated by Barrodale and Erickson (1980) algorithm adopted to complex-valued time series by Brzeziński (1994). The mean FTBPF amplitude spectra computed for more narrow frequency bandwidth than time variable FTBPF amplitude spectra of the differences between pole coordinate data and their LS+AR predictions at 2, 4 and 8 weeks in the future show the peaks for residual prograde Chandler and annual oscillations (Fig.…”

Data Adaptive Spectral Analysis of Unsteady Leakage Flow in an Axial Turbine

“…Later Ulrych and Clayton [18] reviewed the principles of maximum entropy spectral analysis and the closely related topic of autoregressive time series modeling. Barrodale and Erickson [19,20] developed an algorithm to solve the underlying least-squares linear prediction problem in maximum entropy spectral analysis. At the same time, Theodoridis and Cooper [21] applied the maximum entropy spectral analysis technique to signals with spectral peaks of finite width and compared their results to that of the conventional Fourier method.…”